A study on the cross-application of fractal geometry and garden design aesthetics

Currently there is a lack of research on garden design combined with fractal geometry, and most of the research results remain in qualitative analysis and subjective analysis. In this paper, we quantitatively analyze garden design based on fractal geometry to promote the development and innovation of aesthetics in garden design. Based on the reading of literature and other materials, the theory of fractal geometry and its application in the field of garden design are summarized. Based on Gabriel Lame’s design, we constructed the basic unit shape and layout representation using AutoCAD software to realize mathematical modeling design. A good fit of plant fractal dimension was indicated by the coefficient of determination of plant fractal dimension in the study subject garden being 0.9583. Based on the known logN(r) and log(1/r) of 0.1563 and 0.1013, respectively, the value of the fractal dimension of the garden site was derived as 1.54294 by applying the corresponding formula.The regression equation for the contribution of the fractal dimension of each element of the landscape of the mountains and rocks = 0.118-0.0407*Wigwam + 0.277*Wigwam and building combination+0.438*Wigwam and plant combination-0.019*Building+0.306*Building and plant combination-0.022*Plant, and the model R² is 0.863. This study not only provides reference for future design and quantitative analysis of the antique gardens, but also provides new ideas for the construction of a better human environment and landscaping works.